Analytical simulation of the inflation process of inflatable structures is key to assessing their robust deployment in a space environment. Although the problem seems to be intractable, a simplified finite volume inflation model is developed, which allows discretized description of the gas flow, pressure variation, and resulting nonlinear large deformation throughout domains of the inflatable structure. Simulation results are presented along with convergence studies, which provide insight into the deployment of three different packaging/deployment schemes: Z-unfolding, rollout, and extrusion of a cylindrical tube. The proposed inflation model is not limited to prismatic one-dimensional components and can be applied to inflatable shapes with complex configurations. As a validation of the numerical simulation, a laboratory experiment was conducted on the Z-folded configuration. Generally, good agreement in the overall inflation dynamics is observed between the analysis and experiment.